Drive/disto through cabs equiped with tweeters

I'm aiming to afford myself a drive/disto pedal/preamp (whatever). Still I've heard that the types of effect don't match well with cabs equiped with tweeters as tweeters tend to catch the worst frequencies from it. Is it true?
I own 2 SWR Goliath III and want to make sure, the sound will be good at least

I was planning to put the effect in the effect loop to send the distorded signal to only one cab, tweeter off, using the stereo feature of my SVT4 Pro. The other one would remain clear. But drives and distos don't go well in FX loops I was told.

My small rig is a fender rumble 350 and rumble 2x10 and 1x12. Both have tweeters with on, off, and -6db switches. I usually turn one off and leave the other on at -6db. I like the tweeter for my clean tone so it is present, but then when I start to use drives they don't get screechy.

No it doesn't!!!
I always keep it at 25% at least. It provides that very particular crystal clear sound that is typical at SWR (and probably the same for Eden and EBS). Espacially for slap!!
No offense here it's just my point of view